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lfunc_lfunctions • Show schema
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{'Lhash': '2335353431031635545863662342093', 'a10': [0.7471465723754253, -9.969978134204123], 'a2': [-3.3844299129653024, -2.6989927921274193], 'a3': [4.571169448853837, 30.327727690226034], 'a4': [-10.07153602938556, -44.12628249852915], 'a5': [1.301047424217362, 1.908286086612109], 'a6': [66.38351581758917, -114.97962218111665], 'a7': [-187.2059915014023, 108.08342958724542], 'a8': [-205.2159923710585, 426.1353990773283], 'a9': [-202.26290130427165, 62.38984239589038], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.892325595653594, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [79370.49442972752, 4657.001501029632]]]], 'bad_primes': [43], 'central_character': '43.19', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '492194679628176344580305125083', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.3844299129653024, 2.6989927921274193], [14.241339773204121, 62.39538637963671]], 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'-0.4059515089661513 + 0.913894617758582*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.316529909277', 'prec': 47}, 'spectral_label': 'c6-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84226902161461177840695418348', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.02004499920606462428840830751', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.69796021520132941273280365873', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.892325595653594, 'bad_primes': [43], 'central_character': '43.19', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/7/h/a/19/8'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-43-43.19-c6-0-13', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-43-43.19-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.1452067651672113, 'root_angle': 0.31652990927742675, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84226902161461177840695418348', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2335353431031635545863662342093', 'Lhash_array': ['2335353431031635545863662342093'], 'factors': ['2-43-43.19-c6-0-13'], 'label': '2-43-43.19-c6-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/7/h/a/19/8'}